What is 2/27 plus 2/21? (Answer: 32/189)

Exact Answer

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Problem: What is 2/27 plus 2/21?
Formula / Expression: 2/27 + 2/21
Final Answer: 32/189
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).
Working: LCD(27, 21) = 189

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 2/27 by 7, and multiply the numerator and denominator of 2/21 by 9 so both fractions share the common base 189.
Working: 2 × 7/27 × 7 = 14/189 and 2 × 9/21 × 9 = 18/189

Step 3: Add the Numerators
Now add the numerators (14 + 18 = 32) and keep the common denominator 189 unchanged.
Working: 14 + 18/189 = 32/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 32 and 189 is 1, confirming that 32/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 32/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 189 produces a repeating decimal (approximately 0.169312, or 16.9312%).
Working: 32 ÷ 189 = 0.169312 (16.9312%)

Key Values:
- Simplified Fraction: 32/189
- Mixed Number Form: 32/189
- Decimal Value: 0.169312
- Percentage: 16.9312%

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Solved with FractionsCalc:
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2/27 + 2/21 = 32/189

Simplified Fraction

32/189

Mixed Number

Proper (32/189)

Decimal Value

0.169312

Percentage

16.9312%

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Step-by-Step Solution: 2/27 + 2/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).

LCD(27, 21) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 2/27 by 7, and multiply the numerator and denominator of 2/21 by 9 so both fractions share the common base 189.

2 × 7/27 × 7 = 14/189 and 2 × 9/21 × 9 = 18/189

Step 3

Add the Numerators

Now add the numerators (14 + 18 = 32) and keep the common denominator 189 unchanged.

14 + 18/189 = 32/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 32 and 189 is 1, confirming that 32/189 cannot be reduced further—it is already in its simplest irreducible form.

32/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 189 produces a repeating decimal (approximately 0.169312, or 16.9312%).

32 ÷ 189 = 0.169312 (16.9312%)

Visual Representation

The diagram below illustrates 2/27 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/189`
Mixed Number Form	`32/189`
Decimal Form	`0.169312`
Percentage	`16.9312%`

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Frequently Asked Questions

What is 2/27 plus 2/21 as a fraction?

2/27 + 2/21 in simplest fraction form is 32/189.

What is 2/27 plus 2/21 as a decimal?

2/27 + 2/21 converted to a decimal is 0.169312.

What is 2/27 plus 2/21 as a percentage?

2/27 + 2/21 expressed as a percentage is 16.9312%.

Does 2/27 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.169312...) because the denominator contains prime factors other than 2 and 5.